1. Field of the Invention
The present invention relates to a fluorescent X-ray analyzing method and an apparatus thereof. More particularly, the present invention relates to a new fluorescent X-ray analyzing method and a new fluorescent X-ray analyzing apparatus which can perform profile fitting to an energy spectrum with a high degree of freedom and with great precision.
2. Description of the Related Art
Conventionally, for quantitative analysis or qualitative analysis of a sample, there is used a fluorescent X-ray analyzing method which employs fluorescent X-rays generated from the sample by irradiation of X-rays (primary X-rays) or particle beams such as neutron beams or electron beams. This fluorescent X-ray analyzing method can be roughly divided into a wavelength dispersive type and an energy dispersive type.
In the wavelength dispersive type, fluorescent X-rays generated from a sample are adjusted into a parallel beam by a Soller slit, and then it is made an X-ray spectrum dispersed for respective wavelengths by a dispersion system provided with an spectral crystal and a detector. The atomic species (element) content in the sample, atomic species analysis in the sample, and the like are then obtained from the wavelength and intensity of the X-ray spectrum. On the other hand, in the energy dispersive type, fluorescent X-rays are directly detected by a semiconductor detector, which provides an output signal pulse of pulse height value in proportion to the energy of the primary X-rays. The output signal pulse is then electrically separated for every energy of the primary X-rays by a pulse height analyzer, thereby to obtain an energy spectrum, and a sample analysis is performed from the peak of this energy spectrum.
The wavelength dispersive type has merits that an energy resolution is high, and a P/B ratio and precision of quantitative analysis are superior, whereas it has defects that a measurement time is long since the measurement is performed while moving at every constant angle. Also, the wavelength dispersive type needs a moving mechanism and precise operation such as rotation of the detector around the spectral crystal, and its analyzing apparatus is very large in size. On the other hand, since the energy dispersive type detects fluorescent X-rays directly by the semiconductor detector without using any spectral crystals or the like as described above, it can measure the X-ray spectrum of a wide range of energy at the same time. Also, the efficiency of the detector is very high, and its analyzing apparatus is small in size, so that it is very preferable in the site of research and development requiring effective use of space. However, the energy dispersive type having such superior features has a defect that an energy resolution is low as compared with the wavelength dispersive type.
Fluorescent X-rays are X-rays which are generated from each atomic species contained in a sample irradiated with primary X-rays of a certain energy or more and have energy intrinsic to each atomic species. Thus, by comparing the intensity of fluorescent X-rays from a certain atomic species with that of fluorescent X-rays from another atomic species, the content ratio of the atomic species in the sample can be obtained. However, in spite of the feature that the fluorescent X-rays originally have dispersion of a very narrow width with respect to the energy, they are observed as a peak having a large width because of the capacity of the detector (circuit) decomposing the received energy and because of other uncertain factors. Therefore, since the width of the peak is widened, there have been problems that although integration intensities of every independent peaks ought to be obtained in the case where the peak energies of the respective atomic species in the sample are widely separated from one another, the peaks overlap with one another so that it becomes difficult to obtain a separated intensity ratio, and also in the case where the peaks have energies close to one another, an overlapping portion is originally produced to some degree, but the overlapping portion becomes further remarkable. Especially, the energy dispersive type is inferior to the wavelength dispersive type in capacity of separating adjacent peak energies from each other, thus overlapping occurs more remarkably than the wavelength dispersive type, and the energy resolution is low.
Then, in order to compensate lowering of analyzing precision caused by such low energy resolution, a technique called profile fitting (or whole pattern fitting) is often used.
This profile fitting is one of methods of extracting a physical quantity from data having a peak-shaped signal. In the fluorescent X-ray analyzing method, with respect to a sample to be analyzed, a spectrum of each atomic species to be measured is simulated in advance, and fitting of the simulated spectrum with respect to an measured energy spectrum is performed, so that a content ratio of an atomic species having the simulation spectrum matched with the measured energy spectrum, and the like are obtained.
Here, the profile fitting in the fluorescent X-ray analyzing method will be further described.
In the profile fitting, in order to simulate an energy spectrum of a single atomic species in advance, it is necessary to introduce not only physical parameters but also simulation parameters to all conceivable error factors such as mechanical, electrical, and geometrical factors. Then, values of parameters at which the result of the simulation is closest to measurement values are determined by the least square method. However, with respect to a fine shape of each peak, the influence from a mechanical and electrical system is large, and there is a possibility that the shape changes for each apparatus and also changes with time. Thus, it is very difficult to accurately simulate all energy spectra of which the shapes change like this. Accordingly, a simulation spectrum is replaced by a function which relatively simply expresses an energy profile, a so-called profile function, thereby attempting to express various profile shapes by parameter values of the profile function.
FIG. 1 shows an example of an energy spectrum symmetrical with respect to a peak position. Here, the profile function is made P (param;e) as a function searching for a parameter group (param) which is for expressing an energy profile and an intensity of energy (e).
A simplest example of a profile analysis relates to one energy peak. In this case, parameters are a position e, of the peak and scale factor s. This is, as indicated in Eq.1, by setteing a profile function at some position and multiplying the whole with the scale factor s, the energy spectrum I(e) of the single peak can be expressed.
xe2x80x83I(e)=Sxc2x7P(param,c=t0)xe2x80x83xe2x80x83(Eq.1)
Then, the peak position and the value of the scale factor, together with the parameters of the profile function, are changed to search for values matching the actual peak. FIG. 2 shows an example of this single peak fitting (in the drawing, xe2x80x9cresidualxe2x80x9d indicates an error between a measured value and a calculated value). Further, when the integral value of the profile function is 1, the scale factor itself expresses an integration intensity. In the case where there are two peaks as exemplified in FIG. 3, two profile functions, each having own scale factor and peak position, are prepared, and all parameters are to be matched. Then, the respective scale factors become xe2x80x9cseparated integration intensityxe2x80x9d. Even if peaks are further increased, the same is true, and this can be expressed by Eq. 2.
I(e)=S1xc2x7P(param;exe2x88x92e1)+S2xc2x7P(param,e=e2)xe2x80x83xe2x80x83+(Eq.2)
However, there occur such problems that when parameters increase, it becomes difficult to obtain an answer. Thus, it becomes important to study the feature of fluorescent X-rays carefully and estimate what is known and what can be eliminated from the parameters. First, a fluorescent X-ray which is energy emitted from a certain atomic species has a specified value which never changes. This means that the peak position needs not to be changed. In addition, the number of fluorescent X-rays emitted from one atomic species is definite, and the ratio of intensities does not change at every measurement. Thus, the energy and relative intensity can be prepared as a table. Thus, the energy and relative intensity can be prepared as a table. Based on these features, it is preferable to decrease the number of parameters to the utmost.
First, a spectrum caused from one atomic species is considered. Based on a table of energy ej,k of a fluorescent X-ray k of a certain atomic species j and relative intensity Ij,k, a spectrum Ij(e) is prepared by assigning a profile function to each peak. This can be expressed by Eq.3, and FIG. 4 shows an example of a spectrum from a single atomic species prepared in this way.                               I                      j            ⁡                          (              e              )                                      =                              ∑            k            peak                    ⁢                                    I                              j                ,                k                                      ·                          P                              (                                  param                  ;                                      e                    =                                          e                                              j                        ,                        k                                                                                            )                                                                        (                  Eq          .                      xe2x80x83                    ⁢          3                )            
Here, it is assumed that the peak shapes are the same for all peaks, and only one parameter set of a profile is defined in common (it is defined in common also among atomic species). Parameter sets are prepared for all atomic species needed to be analyzed, and a scale factor sj for each atomic species is defined, and this is made a parameter as in Eq.4. FIG. 5 shows an example of superposition of spectra I(e) obtained from Eq.4 for spectra from two atomic species.                               I                      (            e            )                          =                              ∑            j            atom                    ⁢                                    s              j                        ·                          I                              j                ⁡                                  (                  e                  )                                                                                        (                  Eq          .                      xe2x80x83                    ⁢          4                )            
Thus, it is the scale factor sj of each atomic species and the parameter as to the profile that to be optimized. And, the ratio of the scale factor becomes the ratio of integration intensity for each atomic species as it is.
In the foregoing profile fitting, Gaussian function and Lorentz function are conventionally used as the profile function P(param;e). As exemplified by Eqs. 5a and 5b and FIG. 6, the Gaussian function attenuates quickly, while the Lorentz function on has its skirts extending over a wide range. A parameter in those functions is a full width at half maximum intensity W.                     Gaussian        ⁢                  xe2x80x83                ⁢        function                            xe2x80x83                                          P                      (                          W              ;              e                        )                          =                  exp          ⁡                      [                                          -                4                            ⁢                                                (                                      e                    W                                    )                                2                                      ]                                              (Eq. 5a)                                Lornetz        ⁢                  xe2x80x83                ⁢        function                            xe2x80x83                                          P                      (                          W              ;              e                        )                          =                              [                          1              +                              4                ⁢                                                      (                                          e                      W                                        )                                    2                                                      ]                                -            1                                              (Eq. 5b)            
There are also known functions having properties of a combination of these two functions. There can be expressed as Eqs.6a and 6b, and are called pseudo-Voight function and Peason VII function. These functions uses a ratio R of contribution of the Gaussian function and the Lorentz function as a parameter, and can express an energy profile having a intermediate shape between the Gaussian function and the Lorentz function as is exemplified in FIG. 7 (in the drawing, it is depicted as xe2x80x9cMIXED FUNCTIONxe2x80x9d).                     psuedo        ⁢                  -                ⁢        Voigt        ⁢                  xe2x80x83                ⁢        function                            xe2x80x83                                          P                      (                          W              ,                              R                ;                e                                      )                          =                                            (                              1                -                R                            )                        ·                                          [                                  1                  +                                      4                    ⁢                                                                  (                                                  e                          W                                                )                                            2                                                                      ]                                            -                1                                              +                      R            ·                          exp              ⁡                              [                                                      -                    4                                    ⁢                                                            (                                              e                        W                                            )                                        2                                                  ]                                                                        (Eq. 6a)                                Peason        ⁢                  xe2x80x83                ⁢        VII        ⁢                  xe2x80x83                ⁢        function                            xe2x80x83                                          P                      (                          W              ,                              R                ;                e                                      )                          =                              [                          1              +                              4                ⁢                                  (                                                            2                                              1                        R                                                              -                    1                                    )                                ⁢                                                      (                                          e                      W                                        )                                    2                                                      ]                                -            R                                              (Eq. 6b)            
However, all these conventional profile functions express energy profiles symmetrical with respect to the peak positions (that is, a profile in which a low energy side and a high energy side become symmetrical with respect to the peak position). Consequently, in the conventional sample analysis, although analysis precision is high for an atomic species generating a fluorescent X-ray of a symmetrical energy spectrum having a symmetrical shape with respect to the peak position, analysis precision is extremely low for an atomic species generating a fluorescent X-ray of asymmetrical energy spectrum having an asymmetrical shape with respect to the peak position since fitting to the asymmetrical energy spectrum has naturally a large error. Thus, a satisfactory analysis result can be obtained only for a sample which is predicted to have only atomic species generating fluorescent X-rays of symmetrical energy spectra. This prevents the improvement of the analysis precision and the degree of freedom in the fluorescent X-ray analyzing method, especially in the energy dispersive type.
In view of the foregoing, it is the main object of the present invention to provide a new fluorescent X-ray analyzing method and an apparatus thereof which can perform a superior quantitative and qualitative analysis even for an atomic species generating a fluorescent X-ray of an asymmetrical energy spectrum, and can remarkably improve the analysis precision and the degree of freedom of a fluorescent X-ray analysis.